In the first part of this thesis, we proved a pseudo-locality theorem for a coupled Ricci flow, extending Perelman’s work on Ricci flow to the Ricci flow coupled with heat equation. By use of the reduced distance and the pseudo-locality theorem, we showed that the parabolic rescaling of a Type I coupled Ricci flow with respect to a Type I singular point converges to a non-trivial Ricci soliton. In the second part of the thesis, we prove the existence of infinitely many solutions to the Hull- Strominger system on generalized Calabi-Gray manifolds, more specifically compact non-K \"ahler Calabi-Yau 3-folds with infinitely many distinct topological types and sets of Hodge numbers. We also studied the behavior of the anomaly flow on the generalized Calabi-Gray manifolds, and reduced it to a scalar flow on a Riemann surface. We obtained the long-time existence and convergence after rescaling in the case when the curvature of initial metric is small.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/D8WH4642 |
| Date | January 2018 |
| Creators | Huang, Zhijie |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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